Molecular conformation of polyelectrolytes inside Layer-by-Layer assembled films

Among all methods available for the preparation of multifunctional nanostructured composite materials with remarkable functional properties, Layer-by-Layer (LbL) assembly is currently one of the most widely used techniques due to its environmental friendliness, its ease of use and its versatility in combining a plethora of available colloids and macromolecules into finely tuned multicomponent architectures with nanometer scale control. Despite the importance of these systems in emerging technologies, their nanoscopic 3D structure, and thus the ability to predict and understand the device performance, is still largely unknown. In this article, we use neutron scattering to determine the average conformation of individual deuterated polyelectrolyte chains inside LbL assembled films. In particular, we determine that in LbL-films composed of poly(sodium 4-styrenesulfonate) (PSS) and poly(allylamine hydrochloride) (PAH) multilayers prepared from 2 M sodium chloride solutions the PSS chains exhibit a flattened coil conformation with an asymmetry factor of around seven. Albeit this highly non-equilibrium state of the polymer chain, its density profiles follow Gaussian distributions occupying roughly the same volume as in the bulk complex.

In order to determine whether films prepared in the same conditions lead to the same structure and to study the reproducibility of the film build-up, we decided to use the "Global Fit" option of Motofit [1]. O. Félix et al. [2] already investigated this idea by determining the structural parameter values from two films either fully deuterated or fully protonated. They observed that it is possible to use structural values of some other films prepared in the same S2 conditions, but not for all them. In our case, we went further by using the "Global Fit" process, which allows to fit several reflectivity curves at the same time, with the possibility to link the parameters of the different films together, so that one value of the parameters is calculated for all the films. For example, it is possible to determine one value of the thickness per layer pair for all the films. Then, by comparing the global fit results with the individual fits, it is possible to determine if the parameters are the same for all the films or not.
For this study, we analysed the specular reflectivity curves measured at LLB in 2007[2] for the sixteen multilayer films prepared by spraying in the same conditions :    In addition we report in Supplementary Tab. II the fitting parameters for the curve shown in Fig. 1a of the main article. The multilayer structure is [(PSS 70%d7 -PAH) 73 prepared by dipping.
Finally, we report a specular reflectivity curve of a sample stored for 15 years at ambient conditions with the following structure: [(PSS h7 -PAH) 2 /(PSS d7 -PAH)] 8 . In Supplementary Fig. 5 it can be seen that the Bragg-peak related to the inserted deuterated layers is still present, testifying the effective "freezing" of non-equilibrium structures in these solid-like films.

Isotope effects in SANS
The theoretical scattering cross section under the assumption of slight incompatibility of deuterated and protonated chains is given by the Random Phase Approximation [3]:

S6
Here, v e is the excluded volume parameter or second virial coefficient in case of deviations from the ideal Gaussian chain. In essence, if slight isotope effects are taken into account the total cross-section of the single chain form factor keeps its original shape, but the toal cross-section at zero q would be overestimated by a simple homogeneous Fit (eq. 2). In the here studied case the molecular weight of 80800 g/mol is relatively low and thus isotope effects are unlikely to play a significant role.
Estimation of free radius of gyration of PSS in complexes M. Z. Markarian et al. have studied the size of PSS chains in bulk complexes of polyelectrolytes [4]. The radius of gyration of PSS chains in a PSS/(diallyldimethylammonium chloride) (PDADMAC) complex was determined by SANS, for two different molecular weights of the PSS (M w = 14000 g/mol and M w = 104000 g/mol) and for concentration of salt (sodium chloride, NaCl) in the solutions from 0.1 M to 1.5 M. The conformations were determined to be more or less spherical, and the sizes were 25Å to 27Å for the low PSS molecular weight and 105Å to 110Å for the high PSS molecular weight. Taking the radius of gyration of the 104000 g/mol PSS in a 2 M NaCl PDADMA complex as a starting point and scaling to our molecular weight of 80,800 g/mol we can estimate the bulk radius of gyration of the PSS in the complex being around 90Å in our case.

Details of the SANS modeling
In analogy to previous SANS studies on polyelectrolyte/salt complexes [5] we opted for a model consisting of three distinct contributions: The scattering from fractals at low q-values, the scattering from single polymer chains at larger q-values and a flat background due to incoherent scattering at the largest q values. This was accomplished either by using the fitting program SASFit [6] or by using a hand-written code as explained later. In SASFit the low-q region was modeled as a mass fractal and the best fit for the dipped sample was obtained with an exponential cut-off correlation length of ξ = 850Å and a gauge of r 0 = 81Å and a fractal dimension of D = 2 pointing towards a random walk structured agglomerate. The sprayed sample showed stronger fractal scattering and was best fitted with a correlation length of 1230Å, a gauge of 46Å and a fractal dimension of D = 2.95, reveling more clustered and larger agglomerates. We note here that different samples prepared the same way showed different scattering in this low q region, pointing towards a non-reproducible character of these fractal structures even among different samples prepared the same way. The generally stronger fractal scattering of the sprayed samples compared to the dipped ones was always observed, though. However, whatever the exact fractal parameters used to model these large structures the fitting results for the smaller sized structures were only little influenced, at least for the dipped samples. In SASFit we used two approaches to fit the higher q-region of the SANS curves: a) Either a worm-like chain model (e.g. Kholodenko worm) was used to fit this entire range, which allowed to fit the chain contour length, the Kuhn length (b) and the scattering contrast, or, b) a sum of two contributions with the smaller size contribution responsible for the high-q region showing a power law of -1, modeled as a freely joined chain of (infinitely thin) rods of a fitted Kuhn length and arbitrarily fitted scattering strength and a second contribution for intermediate sizes, modeled as a Gaussian distribution of (point-like) monomers resulting in the well-known Debye-function if Fourier-transformed into q-space. In both of these approaches the best fit was obtained assuming a Kuhn length of 10Å for all samples, recovering the known Kuhn length for PSS [7]. The single-chain radius of gyration in direction parallel to the surface for the dipped sample turned out to be R ∥ g = 140 ± 20Å for the worm-like chain model and R ∥ g = 180 +20 −10Å for the Debye fit, the latter being well in accord with the model-free Guinier analysis presented above. The absolute intensity of this contribution turned out to be 20 ± 3 cm −1 in the worm-like chain model and 16 ± 4 cm −1 for the Debye fit, both being within the theoretical values extracted from the neutron scattering contrast between the deuterated and protonated PSS chains, their concentration and molecular weight as explained in the Methods section. For the sprayed sample the wormlike chain model revealed the same value for R ∥ g (140Å) and scattering intensity (20 cm −1 ), whereas the Debye model fitted R ∥ g = 220Å with a scattering contrast of 18 cm −1 for the sprayed sample. Alternatively, we used a home-written code to fit the SANS curves using the approach presented in Refs. [7,8], often used for PE solutions which assumes infinitely long worm-like chains resulting in the asymptotic behaviour calculated by de Cloizeaux. Here we also added a constant background and the fractal part as in SASFit. The exact used function is presented in the Methods section. Using this approach the fitting results tuned out to be rather ambiguous, though. The best fit for the fractal scattering was achieved using D = 2.5, r 0 = 130Å and ξ = 380Å for the dipped sample and D = 2.93, r 0 = 49Å and ξ = 1300Å for the sprayed sample rather consistent with the SASFit analysis. The effective monomer length turned out to be significantly larger than for bulk PSS (a ∼ 2Å) and could be fitted to 4Å for the dipped sample and 5Å for the sprayed one. The persistence length turned out to be 87Å for the dipped sample, which is also larger than values reported in pure PSS solutions (36Å < l p < 77Å), reflecting the qualitative result obtained from the power law change-over momentum transfer discussed above. For the sprayed samples l p = 41Å gave the best fit, this value, however, has to be taken with care as accompanied with a large uncertainty due to the strong small q scattering. Similarly for the radius of gyration, the analysis of the dipped sample revealed a value of 230±60Å, while for the sprayed one R ∥ g = 150Å showed the best fit (both with a scattering contrast around 25 cm −1 ). But again, the radius of gyration came in with a very large fitting error and a value of R ∥ g = 180Å fitted both of the data equally well. In general, due to the strong low q scattering of the sprayed samples (and spin-coated samples, not shown), the single chain parameters R ∥ g and l p are very difficult to extract as the fractal scattering characterised by a steep q-power law directly turns into the chain stiffness power law (∼ q −1 ) overwhelming the scattering from the entire chain's form (∼ q −2 ). Therefore these parameters extracted from sprayed and spin-coated samples cannot be used and will not be discussed further, only the effective monomer size (a) or Kuhn length (b) could be extracted from these samples.

GISANS
The experimental curves for the three wavelengths falling onto a master curve are shown in Supplementary Figure  6.
Supplementary Figure 6: Out-of-plane scans (GISANS Intensity vs q y [Å −1 ]) of the multilayer film of 53 bi-layers containing 50% deuterated PSS. The experimental data (points) for average wavelengths of 4Å, 5Å and 7Å are shown. The line is a fit to the low q data reveling a power law with a slope of -2. Error bars indicate the statistical counting error.
The Guinier analysis of the same GISANS data at 11Å wavelength is shown in Supplementary Fig. 7.